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NumericalAlgebraicGeometry :: regeneration(List)

regeneration(List) -- solve a system of polynomial equations with regeneration method

Synopsis

Description

Regeneration is a blackbox method that obtains a numerical describtion of an algebraic variety. Note that Ws are not necessarily irreducible witness sets; use decompose(WitnessSet) to decompose into irreducibles.
setRandomSeed 7
R = CC[x,y]
F = {x^2+y^2-1, x*y};
regeneration F
R = CC[x,y,z]
sph = (x^2+y^2+z^2-1);
I = ideal {sph*(x-0.5)*(y-x^2), sph*(y-0.5)*(z-x^3), sph*(z-0.5)*(z-x^3)*(y-x^3)};
cs = regeneration I_*

Caveat

This function is under development. It may not work well if the input represents a nonreduced scheme.The (temporary) option Output can take two values: Regular (default) and Singular. It specifies whether the algorithm attempts to keep singular points.

See also